Abstract

For the real-time computation of computer-generated holograms (CGHs), various accelerated algorithms have been actively investigated. This paper proposes a novel concept of sparse computation of polygon CGH, which is inspired by an observation of the sparsity in the angular spectrum of a unit triangular polygon and present the accelerated algorithm using the intrinsic sparsity in the polygon CGH pattern for the enhancement of computational efficiency effectively. It is shown with numerical results that computation efficiency can be greatly improved without degrading the quality of holographic image.

© 2015 Optical Society of America

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Semi-analytic texturing algorithm for polygon computer-generated holograms

Wooyoung Lee, Dajeong Im, Jeongyeup Paek, Joonku Hahn, and Hwi Kim
Opt. Express 22(25) 31180-31191 (2014)

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2014 (4)

2013 (3)

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref] [PubMed]

Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52(1), A290–A299 (2013).
[Crossref] [PubMed]

R. Stahl, V. Rochus, X. Rottenberg, S. Cosemans, L. Haspeslagh, S. Severi, G. V. Plas, G. Lafruit, and S. Donnay, “Modular sub-wavelength diffractive light modulator for high-definition holographic displays,” J. Phys. Conf. Ser. 415, 012057 (2013).
[Crossref]

2012 (3)

2011 (1)

2010 (4)

2009 (1)

2008 (2)

R. Haussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE 6803, 68030M (2008).
[Crossref]

H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. 47(19), D117–D127 (2008).
[Crossref] [PubMed]

2005 (1)

1988 (1)

Aoshima, K.

K. Aoshima, N. Funabashi, K. Machida, Y. Miyamoto, K. Kuga, T. Ishibashi, N. Shimidzu, and F. Sato, “Submicron magneto-optical spatial light modulation device for holographic displays driven by spin-polarized electrons,” J. Disp. Tech. 6(9), 374–380 (2010).
[Crossref]

Awazu, S.

Chen, B.-C.

Chen, N.

Cho, J.

Choi, H.-J.

Cosemans, S.

R. Stahl, V. Rochus, X. Rottenberg, S. Cosemans, L. Haspeslagh, S. Severi, G. V. Plas, G. Lafruit, and S. Donnay, “Modular sub-wavelength diffractive light modulator for high-definition holographic displays,” J. Phys. Conf. Ser. 415, 012057 (2013).
[Crossref]

Dong, J.-W.

Donnay, S.

R. Stahl, V. Rochus, X. Rottenberg, S. Cosemans, L. Haspeslagh, S. Severi, G. V. Plas, G. Lafruit, and S. Donnay, “Modular sub-wavelength diffractive light modulator for high-definition holographic displays,” J. Phys. Conf. Ser. 415, 012057 (2013).
[Crossref]

Frère, C.

Funabashi, N.

K. Aoshima, N. Funabashi, K. Machida, Y. Miyamoto, K. Kuga, T. Ishibashi, N. Shimidzu, and F. Sato, “Submicron magneto-optical spatial light modulation device for holographic displays driven by spin-polarized electrons,” J. Disp. Tech. 6(9), 374–380 (2010).
[Crossref]

Fütterer, G.

Hahn, J.

Haspeslagh, L.

R. Stahl, V. Rochus, X. Rottenberg, S. Cosemans, L. Haspeslagh, S. Severi, G. V. Plas, G. Lafruit, and S. Donnay, “Modular sub-wavelength diffractive light modulator for high-definition holographic displays,” J. Phys. Conf. Ser. 415, 012057 (2013).
[Crossref]

Haussler, R.

R. Haussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE 6803, 68030M (2008).
[Crossref]

Häussler, R.

He, H.-X.

Hong, J.

Hosseini, E. S.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref] [PubMed]

Hwang, C.-Y.

Ichihashi, Y.

Im, D.

Ishibashi, T.

K. Aoshima, N. Funabashi, K. Machida, Y. Miyamoto, K. Kuga, T. Ishibashi, N. Shimidzu, and F. Sato, “Submicron magneto-optical spatial light modulation device for holographic displays driven by spin-polarized electrons,” J. Disp. Tech. 6(9), 374–380 (2010).
[Crossref]

Ito, T.

Jia, J.

Kanbayashi, Y.

Kato, H.

Kim, H.

Kim, K.-S.

Kim, S.

Kim, Y.

Kuga, K.

K. Aoshima, N. Funabashi, K. Machida, Y. Miyamoto, K. Kuga, T. Ishibashi, N. Shimidzu, and F. Sato, “Submicron magneto-optical spatial light modulation device for holographic displays driven by spin-polarized electrons,” J. Disp. Tech. 6(9), 374–380 (2010).
[Crossref]

Lafruit, G.

R. Stahl, V. Rochus, X. Rottenberg, S. Cosemans, L. Haspeslagh, S. Severi, G. V. Plas, G. Lafruit, and S. Donnay, “Modular sub-wavelength diffractive light modulator for high-definition holographic displays,” J. Phys. Conf. Ser. 415, 012057 (2013).
[Crossref]

Lee, B.

Lee, B.-R.

Lee, D.

Lee, W.

Leister, N.

Leseberg, D.

Li, X.

Liu, J.

Liu, Y.-Z.

Machida, K.

K. Aoshima, N. Funabashi, K. Machida, Y. Miyamoto, K. Kuga, T. Ishibashi, N. Shimidzu, and F. Sato, “Submicron magneto-optical spatial light modulation device for holographic displays driven by spin-polarized electrons,” J. Disp. Tech. 6(9), 374–380 (2010).
[Crossref]

Masuda, N.

Matsushima, K.

Min, S.-W.

Miyamoto, Y.

K. Aoshima, N. Funabashi, K. Machida, Y. Miyamoto, K. Kuga, T. Ishibashi, N. Shimidzu, and F. Sato, “Submicron magneto-optical spatial light modulation device for holographic displays driven by spin-polarized electrons,” J. Disp. Tech. 6(9), 374–380 (2010).
[Crossref]

Moon, E.

Moon, W.

Nakahara, S.

Nakamura, M.

Nakayama, H.

Oh, S.

Oikawa, M.

Okada, N.

Paek, J.

Pan, Y.

Park, J.-H.

Park, Y.

Plas, G. V.

R. Stahl, V. Rochus, X. Rottenberg, S. Cosemans, L. Haspeslagh, S. Severi, G. V. Plas, G. Lafruit, and S. Donnay, “Modular sub-wavelength diffractive light modulator for high-definition holographic displays,” J. Phys. Conf. Ser. 415, 012057 (2013).
[Crossref]

Pu, Y.-Y.

Reichelt, S.

Rochus, V.

R. Stahl, V. Rochus, X. Rottenberg, S. Cosemans, L. Haspeslagh, S. Severi, G. V. Plas, G. Lafruit, and S. Donnay, “Modular sub-wavelength diffractive light modulator for high-definition holographic displays,” J. Phys. Conf. Ser. 415, 012057 (2013).
[Crossref]

Roh, J.

Rottenberg, X.

R. Stahl, V. Rochus, X. Rottenberg, S. Cosemans, L. Haspeslagh, S. Severi, G. V. Plas, G. Lafruit, and S. Donnay, “Modular sub-wavelength diffractive light modulator for high-definition holographic displays,” J. Phys. Conf. Ser. 415, 012057 (2013).
[Crossref]

Sato, F.

K. Aoshima, N. Funabashi, K. Machida, Y. Miyamoto, K. Kuga, T. Ishibashi, N. Shimidzu, and F. Sato, “Submicron magneto-optical spatial light modulation device for holographic displays driven by spin-polarized electrons,” J. Disp. Tech. 6(9), 374–380 (2010).
[Crossref]

Schwerdtner, A.

R. Haussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE 6803, 68030M (2008).
[Crossref]

Severi, S.

R. Stahl, V. Rochus, X. Rottenberg, S. Cosemans, L. Haspeslagh, S. Severi, G. V. Plas, G. Lafruit, and S. Donnay, “Modular sub-wavelength diffractive light modulator for high-definition holographic displays,” J. Phys. Conf. Ser. 415, 012057 (2013).
[Crossref]

Shimidzu, N.

K. Aoshima, N. Funabashi, K. Machida, Y. Miyamoto, K. Kuga, T. Ishibashi, N. Shimidzu, and F. Sato, “Submicron magneto-optical spatial light modulation device for holographic displays driven by spin-polarized electrons,” J. Disp. Tech. 6(9), 374–380 (2010).
[Crossref]

Shimobaba, T.

Shiraki, A.

Stahl, R.

R. Stahl, V. Rochus, X. Rottenberg, S. Cosemans, L. Haspeslagh, S. Severi, G. V. Plas, G. Lafruit, and S. Donnay, “Modular sub-wavelength diffractive light modulator for high-definition holographic displays,” J. Phys. Conf. Ser. 415, 012057 (2013).
[Crossref]

Sun, J.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref] [PubMed]

Takada, N.

Timurdogan, E.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref] [PubMed]

Usukura, N.

Wang, H.-Z.

Wang, Y.

Watts, M. R.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref] [PubMed]

Yaacobi, A.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref] [PubMed]

Appl. Opt. (9)

D. Leseberg and C. Frère, “Computer-generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt. 27(14), 3020–3024 (1988).
[Crossref] [PubMed]

K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44(22), 4607–4614 (2005).
[Crossref] [PubMed]

H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. 47(19), D117–D127 (2008).
[Crossref] [PubMed]

K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48(34), H54–H63 (2009).
[Crossref] [PubMed]

N. Takada, T. Shimobaba, H. Nakayama, A. Shiraki, N. Okada, M. Oikawa, N. Masuda, and T. Ito, “Fast high-resolution computer-generated hologram computation using multiple graphics processing unit cluster system,” Appl. Opt. 51(30), 7303–7307 (2012).
[Crossref] [PubMed]

Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52(1), A290–A299 (2013).
[Crossref] [PubMed]

H. Nakayama, N. Takada, Y. Ichihashi, S. Awazu, T. Shimobaba, N. Masuda, and T. Ito, “Real-time color electroholography using multiple graphics processing units and multiple high-definition liquid-crystal display panels,” Appl. Opt. 49(31), 5993–5996 (2010).
[Crossref]

J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues [Invited],” Appl. Opt. 50(34), H87–H115 (2011).
[Crossref] [PubMed]

H. Kim, C.-Y. Hwang, K.-S. Kim, J. Roh, W. Moon, S. Kim, B.-R. Lee, S. Oh, and J. Hahn, “Anamorphic optical transformation of an amplitude spatial light modulator to a complex spatial light modulator with square pixels [invited],” Appl. Opt. 53(27), G139–G146 (2014).
[Crossref] [PubMed]

J. Disp. Tech. (1)

K. Aoshima, N. Funabashi, K. Machida, Y. Miyamoto, K. Kuga, T. Ishibashi, N. Shimidzu, and F. Sato, “Submicron magneto-optical spatial light modulation device for holographic displays driven by spin-polarized electrons,” J. Disp. Tech. 6(9), 374–380 (2010).
[Crossref]

J. Phys. Conf. Ser. (1)

R. Stahl, V. Rochus, X. Rottenberg, S. Cosemans, L. Haspeslagh, S. Severi, G. V. Plas, G. Lafruit, and S. Donnay, “Modular sub-wavelength diffractive light modulator for high-definition holographic displays,” J. Phys. Conf. Ser. 415, 012057 (2013).
[Crossref]

Nature (1)

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (2)

Proc. SPIE (1)

R. Haussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE 6803, 68030M (2008).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Construction of a holographic 3D image and its CGH pattern by the superposition of (a) the light field elements of unit triangular facets and (b) the elementary sparse angular spectrums of these facets
Fig. 2
Fig. 2 Elementary units of the polygon CGH synthesis algorithm: (a) unit triangular facet and (b) its angular spectrum profile
Fig. 3
Fig. 3 (a) A unit triangle facet in a local coordinate system and its angular spectrum profile in (b) the local coordinate system and (c) in the global coordinate system
Fig. 4
Fig. 4 Construction of the computational ROI: (a) sampled indicator, (b) circular function and (c) ROI
Fig. 5
Fig. 5 (a) Sparse and (b) dense angular spectrums and their reconstruction images of (c) the sparse and (d) dense angular spectrums
Fig. 6
Fig. 6 Simulation setup. The size of CGH is 1921 × 1921 and the distance between the CGH plane and the eye lens plane, F, is set to 800 mm and that between the eye lens and the retina plane, deye, is 25mm. The pixel-pitch of the CGH and the wavelength λ are set to 73µm and 532nm, respectively.. The target object is composed of 10255 triangle facets and is smaller than 45 × 45 × 45mm3. The target object is located near the CGH plane.
Fig. 7
Fig. 7 The reconstructed images and CGH patterns for the ROIs with various sparsity of (a) 1.2014%, (b) 4.0222% and (c) 100%. The average computation times of a unit triangle in the CGH patterns are estimated to (a) 0.0569, (b) 0.2052 and (c) 5.1562 (seconds), respectively, for those cases.
Fig. 8
Fig. 8 (a) Computation time versus the ROI computation region (%) and (b) the computing time used up in the ROI build-up stage.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

( x y z )=( cos θ k cos ϕ k cos θ k sin ϕ k sin θ k sin ϕ k cos ϕ k 0 sin θ k cos ϕ k sin θ k sin ϕ k cos θ k )( x x k y y k z z k ).
W k ( x,y,z )= A G,k ( α,β )exp[ j2π( αx+βy+γz ) ]dαdβ ,
A G,k ( α,β ) = η k A k ( α ( k ) ( α,β ) α 0 ( k ) ( α 0 , β 0 ), β ( k ) ( α,β ) β 0 ( k ) ( α 0 , β 0 ) ) ×H( γ ( k ) ( α,β ) )| cos θ k + sin θ k ( cos ϕ k α+sin ϕ k β ) γ |exp[ j2π{ α( x k )+β( y k )+γ( z k ) } ],
( α β γ )=( cos θ k cos ϕ k sin ϕ k cos ϕ k sin θ k sin ϕ k cos θ k cos ϕ k sin ϕ k sin θ k sin θ k 0 cos θ k )( α β γ ).
t 12 :( x 12 , y 12 )=( ( y 2 y 1 ),( x 2 x 1 ) )s,
t 23 :( x 23 , y 23 )=( ( y 3 y 2 ),( x 3 x 2 ) )s,
t 31 :( x 31 , y 31 )=( ( y 3 y 1 ),( x 3 x 1 ) )s.
l 12 :( α 12 , β 12 )=[ x 12 ( Δα/Δx ), y 12 ( Δβ/Δy ) ]+( α 0 , β 0 ),
l 23 :( α 23 , β 23 )=[ x 23 ( Δα/Δx ), y 23 ( Δβ/Δy ) ]+( α 0 , β 0 ),
l 31 :( x 31 , y 31 )=[ x 31 ( Δα/Δx ), y 31 ( Δβ/Δy ) ]+( α 0 , β 0 ),
A m ( α,β )=F T 1 [ FT( A p ( α,β ) )FT( Circ( α,β ) ) ].

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